OFFSET
1,4
COMMENTS
A rooted tree is series-reduced if no vertex (including the root) has degree 2.
Also labeled lone-child-avoiding rooted trees with n vertices and more than two branches, where a rooted tree is lone-child-avoiding if no vertex has exactly one child.
EXAMPLE
Non-isomorphic representatives of the a(7) = 847 trees (in the format root[branches]) are:
1[2,3,4[5,6,7]]
1[2,3,4,5[6,7]]
1[2,3,4,5,6,7]
MATHEMATICA
lrt[set_]:=If[Length[set]==0, {}, Join@@Table[Apply[root, #]&/@Join@@Table[Tuples[lrt/@stn], {stn, sps[DeleteCases[set, root]]}], {root, set}]];
Table[Length[Select[lrt[Range[n]], Length[#]>2&&FreeQ[#, _[_]]&]], {n, 6}]
CROSSREFS
The non-series-reduced version is A331577.
The unlabeled version is A331488.
Lone-child-avoiding rooted trees are counted by A001678.
Topologically series-reduced rooted trees are counted by A001679.
Labeled topologically series-reduced rooted trees are counted by A060313.
Labeled lone-child-avoiding rooted trees are counted by A060356.
Matula-Goebel numbers of lone-child-avoiding rooted trees are A291636.
Matula-Goebel numbers of series-reduced rooted trees are A331489.
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jan 21 2020
STATUS
approved